Australian AMC 2015 - Intermediate Question 22

Question 22

The square $PQRS$ has sides of length 2 units and $J$ is the midpoint of $PS$. The line $QJ$ intersects the diagonal $PR$ at $L$.

The length of $LP$ is

Question illustration

$\frac{\sqrt2}3$
$\frac{\sqrt3}3$
$\frac{\sqrt2}2$
$\frac{2\sqrt3}3$
$\frac{2\sqrt2}3$